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The purpose of this article is to derive formulas for lifetime expected credit loss of loans that are required for the calculation of loan loss reserves under IFRS 9. This is done both for fixed-rate and floating rate loans under different assumptions on LGD modeling, prepayment, and discount rates.

This study provides exact formulas for lifetime expected credit loss derived analytically together with the mathematical proofs of each expression.

This articles shows that the formula most commonly applied in the literature for calculating lifetime expected credit loss is inconsistent with measuring expected loss based on expected discounted cash flows. Formulas based on discounted cash flows always lead to more conservative numbers.

For banks reporting under IFRS 9, the implication of this research is a better understanding of the different approaches used for computing lifetime expected loss, how they are connected, and what assumptions are underlying each approach. This may lead to corrections in existing frameworks to make applications of risk management systems more consistent.

While there is a lot of literature explaining IFRS 9 and evaluating its impact, none of the existing research has systematically analyzed the calculation of lifetime expected credit loss for this purpose and how the formula changes under different modeling assumptions. This gap is filled by this study.

The changes in women’s and men’s work lives have been considerable in recent decades. Yet much of the recent research on gender differences in employment and earnings has been of a more snapshot nature rather than taking a longer comparative look at evolving patterns. In this paper, we use 50 years (1964–2013) of US Census Annual Demographic Files (March Current Population Survey) to track the changing returns to human capital (measured as both educational attainment and potential work experience), estimating comparable earnings equations by gender at each point in time. We consider the effects of sample selection over time for both women and men and show the rising effect of selection for women in recent years. Returns to education diverge for women and men over this period in the selection-adjusted results but converge in the OLS results, while returns to potential experience converge in both sets of results. We also create annual calculations of synthetic lifetime labor force participation, hours, and earnings that indicate convergence by gender in worklife patterns, but less convergence in recent years in lifetime earnings. Thus, while some convergence has indeed occurred, the underlying mechanisms causing convergence differ for women and men, reflecting continued fundamental differences in women’s and men’s life experiences.

The purpose of this paper is to compute the signature reliability of the coherent systems.

The considered k-out-of-n coherent system consists of n number of elements connected in series. With the help of these systems, the authors have evaluated a mathematical structure using universal generating function.

Using the universal generating function technique, the authors evaluate tail signature, Barlow-Proschan index, expected lifetime and expected cost.

In this paper, the authors have developed a coherent systems based on the universal generating function technique.

This chapter examines the legal and scientific approaches taken in the United States for computing economic damages due to personal injury and wrongful death. The U.S. law of tort damages conforms to a general economic valuation of reduced or lost productivity due to injury under the goal of assigning tort damages optimally so that harm in the society is minimized. Today, “economic damages” are defined in every U.S. jurisdiction, and the field of forensic economics has produced a body of literature concerned with accurately measuring them.

The purpose of this paper is to evaluate the reliability and signature reliability of solar panel k-out-of-n-multiplex system with the help of universal generating function.

Energy scarcity and global warming issues have become important concerns for humanity in recent decades. To solve these problems, various nations work for renewable energy sources (RESs), including sun, breeze, geothermal, wave, radioactive and biofuels. Solar energy is absorbed by solar panels, referred to as photovoltaic panels, which then transform it into electricity that can be used to power buildings or residences. Remote places can be supplied with electricity using these panels. Solar energy is often generated using a solar panel that is connected to an inverter for power supply. As a result, a converter reliability evaluation is frequently required. This paper presents a study on the reliability analysis of k-out-of-n systems with heterogeneous components. In this research, the universal generating function methodology is used to identify the reliability function and signature reliability of the solar array components. This method is commonly used to assess the tail signature and Barlow-Proschan index with independent and identically distributed components.

The Barlow-Proschan index, tail signature, signature, expected lifetime, expected cost and minimal signature of independent identically distributed are all computed.

This is the first study of solar panel k-out-of-n-multiplex systems to examine the signature reliability with the help of universal generating function techniques with various measures.

The purpose of this paper is to evaluate the reliability and structure function of refrigeration complex system consisted of four components in complex manner.

Although, a variety of methodologies have been used to assess the refrigeration system's reliability function that has proven to be effective, the universal generating function approach is the basis of this research study, which is used in the calculation of a domestic refrigeration system with four separate components that are related in series and parallel with a corresponding sample to form a complex machine.

In this paper, signature reliability of the refrigeration system has been evaluated with the universal generating function technique. There are four components present in the proposed system in complex (series and parallel) manner. The tail signature, signature, Barlow–Proschan index, expected lifetime and expected cost of independent identically distributed are all computed.

This is the first study of domestic refrigeration system to examine the signature reliability with the help of universal generating function techniques with various measures. Refrigeration systems are an essential process in industries and home applications as they perform cooling or the maintain temperature at the desired value. A cycle of refrigeration consists of four main components such as, heat exchange, compression and expansion with a refrigerant flowing through the units within the cycle.

The primary purpose of this paper is to develop the translation formula between the required return on unlevered and levered equity for the specific case where cash flows have a finite lifetime and the flow to debt is prespecified. The secondary purpose of this paper is to underpin the importance of the type of stochasticity of cash flows for translation formulas. A general derivation of such formulas and the discount rate in the free cash flow approach is shown.

The paper starts with the same assumptions that have been applied by Modigliani and Miller (1963), Miles and Ezzell (1980) and other researchers. Then the paper develops the mathematical foundations to apply a deterministic backward-iterative scheme for valuing cash flows. After stating the valuation formulas for levered and unlevered equity, debt and tax shields, the authors mathematically derive the relationship between the unlevered return and levered return on equity.

Conventional translation formulas apply to very special cases. They can generally not be used for projects with nonconstant leverage and a finite lifetime. In general, translation formulas depend on continuing values, cash flows, leverage, taxation, risk-free rate, etc. In this paper, the translation depends on the structure of the debt in addition to the well-known parameters in conventional formulas. This paper formula contains the Modigliani-Miller translation formula as a special case.

The authors develop a novel formula for the translation of the required return on unlevered to levered equity. With this formula, the authors offer a solution for the consistent valuation of cash flows with a limited lifetime and given debt financing.

This paper aims to forecast the availability of used but operational electric vehicle (EV) batteries to integrate them into a circular economy concept of EVs' end-of-life (EOL) phase. Since EVs currently on the roads will become obsolete after 2030, this study focuses on the 2030–2040 period and links future renewable electricity production with the potential for storing it into used EVs' batteries. Even though battery capacity decreases by 80% or less, these batteries will remain operational and can still be seen as a valuable solution for storing peaks of renewable energy production beyond EV EOL.

Storing renewable electricity is gaining as much attention as increasing its production and share. However, storing it in new batteries can be expensive as well as material and energy-intensive; therefore, existing capacities should be considered. The use of battery electric vehicles (BEVs) is among the most exciting concepts on how to achieve it. Since reduced battery capacity decreases car manufacturers' interest in battery reuse and recycling is environmentally hazardous, these batteries should be integrated into the future electricity storage system. Extending the life cycle of batteries from EVs beyond the EV's life cycle is identified as a potential solution for both BEVEOL and electricity storage.

Results revealed a rise of photovoltaic (PV) solar power plants and an increasing number of EVs EOL that will have to be considered. It was forecasted that 6.27–7.22% of electricity from PV systems in scenario A (if EV lifetime is predicted to be 20 years) and 18.82–21.68% of electricity from PV systems in scenario B (if EV lifetime is predicted to be 20 years) could be stored in batteries. Storing electricity in EV batteries beyond EV EOL would significantly decrease the need for raw materials, increase energy system and EV sustainability performance simultaneously and enable leaner and more efficient electricity production and distribution network.

Storing electricity in used batteries would significantly decrease the need for primary materials as well as optimizing lean and efficient electricity production network.

Energy storage is one of the priorities of energy companies but can be expensive as well as material and energy-intensive. The use of BEV is among the most interesting concepts on how to achieve it, but they are considered only when in the use phase as vehicle to grid (V2G) concept. Because reduced battery capacity decreases the interest of car manufacturers to reuse batteries and recycling is environmentally risky, these batteries should be used for storing, especially renewable electricity peaks. Extending the life cycle of batteries beyond the EV's life cycle is identified as a potential solution for both BEV EOL and energy system sustainability, enabling more efficient energy management performance. The idea itself along with forecasting its potential is the main novelty of this paper.

The main purpose of this paper is to present an optimal economic solution for a different adaptive sampling method that is highly intuitive in its nature: the normal sampling intervals (NSI) method.

Considering costs associated with sampling, false alarms and imperfect operation per unit of time, the paper presents a new optimal simple solution that minimizes the expected total cost per cycle. This NSI method involves the density function of the standard normal variable, assuming that the distribution of averages is normal or approximately normal (on the basis of the central limit theorem). It depends on a single scale parameter while other methods depend on various parameters.

When this expected total cost associated with the new NSI method is compared with the fixed (FSI) and variable sampling intervals (VSI) methods, in identical situations, it may be seen that, in general, it is lower (and may be much lower) and, also, that it is lower for a wider range of changes in terms of quality. This feature is particularly important because, in practice, the degree of change that occurs is not known, so this greater robustness in terms of performance is relevant.

In the practice, the minimization of total expected costs is an important point of view in the life of companies, concerning quality and statistical process control (SPC). The paper holds that this NSI method has a great degree of potential, in particular considering that in industrial processes there is growing recourse to automated systems for the collection and analysis of samples, and thus there are no special additional costs associated with labour, management or administration.

The great advantages of this NSI method are its highly intuitive nature and the fact that it enables generally much better results to be achieved as compared with the use of FSI and VSI methods. An optimal economic solution for this NSI method is presented in this paper.